Smooth invariants and $\omega $-graded modules over $k[X]$

Fred Richman

Displaying similar documents to “Smooth invariants and $ω$ -graded modules over $k [X]$ ”

Representations of modules over a *-algebra and related seminorms

Camillo Trapani, Salvatore Triolo (2008)

Studia Mathematica

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Representations of a module over a *-algebra $_{}$ are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of $_{}$ .

Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki, Rachid Tribak (2023)

Czechoslovak Mathematical Journal

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We provide some characterizations of rings $R$ for which every (finitely generated) module belonging to a class $𝒞$ of $R$ -modules is a direct sum of cyclic submodules. We focus on the cases, where the class $𝒞$ is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

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We construct a family of non-weight modules which are free $U (𝔥)$ -modules of rank 2 over the $N = 1$ super Schrödinger algebra in $(1 + 1)$ -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free $U (𝔥)$ -modules of rank 2 over $𝔬𝔰𝔭 (1 | 2)$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

Top-stable and layer-stable degenerations and hom-order

S. O. Smalø, A. Valenta (2007)

Colloquium Mathematicae

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Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration $M <_{d e g} N$ such that $^{t} M /^{t + 1} M ≃^{t} N /^{t + 1} N$ for all t. Given a module M with square-free top and a projective cover P, she showed that $d i m_{k} H o m (M, M) = d i m_{k} H o m (P, M)$ if and only if M has no proper degeneration $M <_{d e g} N$ where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from...

The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras

Piotr Dowbor, Andrzej Mróz (2008)

Colloquium Mathematicae

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Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector $m (M) = {(m_{x})}_{x \in X} \in ℕ^{X}$ such that $M ≅ ⨁_{x \in X} X_{x}^{m_{x}}$ is studied. A precise formula for $d i m_{k} H o m_{Λ} (M, X)$ , for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors...

On the composition structure of the twisted Verma modules for $𝔰𝔩 (3, ℂ)$

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

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We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $𝔰𝔩 (3, ℂ)$ , including the explicit structure of singular vectors for both $𝔰𝔩 (3, ℂ)$ and one of its Lie subalgebras $𝔰𝔩 (2, ℂ)$ , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as $D$ -modules on the Schubert cells in the full flag manifold for $SL (3, ℂ)$ .

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

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We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between $n$ -Gorenstein star modules and $n$ -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of $n$ -Gorenstein tilting modules.

Category $𝒪$ for quantum groups

Henning Haahr Andersen, Volodymyr Mazorchuk (2015)

Journal of the European Mathematical Society

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In this paper we study the BGG-categories $𝒪_{q}$ associated to quantum groups. We prove that many properties of the ordinary BGG-category $𝒪$ for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when $q$ is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for $𝒪$ and for finite dimensional $U_{q}$ -modules we are able...

Structure of central torsion Iwasawa modules

Susan Howson (2002)

Bulletin de la Société Mathématique de France

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We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro- $p$ , $p$ -adic, Lie group containing no element of order $p$ . The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro- $p$ subgroups of ${GL}_{2} (ℤ_{p})$ ...

$n$ -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

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Let $R$ be a graded ring and $n \geq 1$ an integer. We introduce and study $n$ -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that $n$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be $m$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever $n > m$ . Many properties of the $n$ -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized....

Lifting $D$ -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

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We study liftings or deformations of $D$ -modules ( $D$ is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic $D$ -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given $D$ -module in positive characteristic. At the end we compare...

Jordan types for indecomposable modules of finite group schemes

Rolf Farnsteiner (2014)

Journal of the European Mathematical Society

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In this article we study the interplay between algebro-geometric notions related to $π$ -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that $π$ -points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on $π$ -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial...

Some Results About Holonomic $ε$ -Modules

Jan-Erik Björk (1983)

Recherche Coopérative sur Programme n°25

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Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

Jon F. Carlson, Nadia Mazza, Jacques Thévenaz (2013)

Journal of the European Mathematical Society

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Let $G$ be a finite group with a Sylow 2-subgroup $P$ which is either quaternion or semi-dihedral. Let $k$ be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial $k G$ -modules, whose restrictions to $P$ are isomorphic to the direct sum of the known exotic endotrivial $k P$ -modules and some projective modules. This provides a description of the group $T (G)$ of endotrivial $k G$ -modules.

Displaying similar documents to “Smooth invariants and ω -graded modules over k [ X ] ”

Displaying similar documents to “Smooth invariants and $ω$ -graded modules over $k [X]$ ”